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Full text of "Conductivity and negative viscosity coefficients of certain rubidium and ammonium salts in glycerol and in mixtures of glycerol with water from 25 to 75.."

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COKDUCTIVITY AlH) NEGATIVE VISCOSITY COEFFICIENTS 
OF CERTAIN RUBIDIUM AKD AMaOHIUM SALTS IH GLYCEROL 
AKD IN MIXTURES OP GLYCEROL WITH WATER 
FROM E5° TO 75° 



DISSERTATION. 



SUBMITTED TO THE BOARD OF UNIVERSITY STUDIES OF TEE 
JOHNS HOPKINS UNIVERSITY IN CONFORMITY WITH 
THE REQUIREIvENTS FOR THE DEGREE OF 
DOCTOR OF PHILOSOPHY 

- by- 

PAUL BELL DAVIS. 



Baltimore, June, 1912. 



/43.3rr 



to 



2^ TA3IE OP CONTEKTS. 

^ Aoknowledgnent o 

Introduotion 1 

Glycerol as a solvent 4 

EXPERILEIITAL . 

Apparatus 10 

Solutions 14 

Solvents 16 

Salts 17 

Procedure 17 

Conductivity Data in Glycerol 19 

" " " Glycerol -water mixtxires 29 

Comparison of Temperature Coefficients 37 

Viscosities and Fluidities in Glycerol 38 

Viscosities and Fluidities in mixed solvents 48 

Per cent increase in Fluidities 56 

DISCUSSION OF RESULTS . 

Conductivity 57 

Negative Viscosity 61 

Conductivity Minima and Negative Viscosity 63 

Per cent coefficients of Fluidity 65 

Summary 66 

Biography 68 



The author accepts this opportunity to express his 
deep sense of gratitude to President Rerasen, to Professor 
Morse, to Professor Jones, to former Professor Eenouf, 
to Professor Swartz.and to Associate Professors Acree, 
Gilpin and Lovelace for valuable advice and instruction 
which have been at all times cheerfully given both in 
the lecture room and laboratory. 

Special thanks are due to Professor Jones, at whose 
suggestion and under v;hose direction this investigation 
was carried out. 

The author also feels under obligation to Drs. Guy 
and V/ightman for kindly advice and assistance. 



INTRODUGTIOH 



The work of Jones and seven of his collaborators, viz., 

1 2 rr 4 K C 

Lindsay, Carroll, Bassett,*-* Bingham, Rouiller, McI>Iaster,° 

and Veasey on the relations between the conductivity and 

viscosity of electrol3''tes in various organic solvents and 

in binary mixtures of these, bas been fully discussed in 

Monograph Mo. 80 of the Carnegie Institution of Washington. 

p 
In addition to this Jones and Schmidt have given a 

complete historical sketch of all the work in mixed sol- 
vents including that which followed the pu.blication of the 

above mentioned monograph. This covered the work carried 

Q 10 

out by Tfe.hin ' and by Ereider. In both of these commu- 

nications due credit has been given to previous workers 
in this field. Therefore, to avoid unnecessary repeti- 
tion, discussion of their results will be taken up only 
in so far as they bear directly on this investigation. 



(1) Amer. Chem. J., 28, 329 (1902). 
(E) Ibid B2, 521 (1904). 

(3) Ibid 32,409 (1904). 

(4) Ibid 34, 481 (1905). 

(5) Ibid 36, 427 (1906). 

(6) Ibid 36, 325 (1906). 

(7) Zeit. f. Phys. Chem., 61, 64 (1908). 

(8) Amer. Chem. J., 42, 37 (1909). 

(9) Zeit. f. rhys. Chem. 69, 389 (1909). 
(10) Amor. Chem. J. 45, 295 (1911). 



The first of these investigators in this laboratory 
to note the phenomenon of negative viscosity was Veazey. 
He measured the conductivity and viscosity of potassium 
sulfocyanate in water, ethyl and methyl alcohols, and 
acetone anc! in binary mixtures of these solvents. In water 
and in certain mixtures of the alcohols with water he noted 
a marked negative viscosity. 

Prior to Yeazey's investigation, Suler had attempt- 
ed to explain the lowering of the viscosity of a solvent 
by a dissolved substance on the basis of the "electrostric- 
tion" of the solvent caused by the charge upon the ions 
of the solute as proposed by Crude and Eernst . 

But Wagner and I!uhlenbein showed that Euler's ex- 
planation v;as not valid since certain non-electrolytes 
in organic solvents also show negative viscosity, e.g., 
cyanobenzol in ethyl alcohol. 

The explanation offered by Jones and Veazey is based 
on their own observations and on the classical 7/ork of 
Thorpe and Roger. ^ The latter have indicated that vis- 
cosity phenomena are in all probability dependent upon 
the frictional surfaces of the ultimate particles present 
in any liquid or solution. A review of the data obtained 



(1) Amer. Ghem. J., 37, 405 (1907). 

(2) Zeit. f. Phys. Ghem. 25, 536 (1898) 

(3) Ibid, 15, 79 (1894). 

(4) Ibid, 46, 867 (1903). 

(5) Phil. Trans., 185-A, 307 (1894). 



by Vi'agner from his study of the viscosity of a number of 
inorganic salts in water vTill show that he found negative 
viscosity only in the case of caesium rubidium and potassium 
salts — and in some instances thallous salts. The first 

three metals occupy the maxima on the atomic volume work 

2 
of Lothar Meyer, i.e., they have the largest atomic vol- 
umes of the elements. That some salts of potassium gave 
positive viscosity is to be expected since it has been 
shown that viscosity is an additive function of both the 
cation and the anion of the dissolved salt. In the case 
in question, the one might tend to lov/er the viscosity 
of the solvent, the other to increase it, the final re- 
sults depending upon whether the sum of these two opposing 
forces was positive or negative. Potassium has the small- 
est atomic volume of the three and in many instances the 
positive viscosity effect of the anion would entirely 
overcome the negative effect of the cation. 

In view of these facts, Jones and Veazey offered the 
apparently satisfactory explanation that "negative vis- 
cosity" is due to a lescening of the skin friction between 
the solvent and the molecules or ions of a solute because 
of the large atomic volume of the cations as compared with 
the molecular aggregates of the solvent. This explanation 
follows directly from the work of Thorpe and Roger. 



(1) Zeit. f. Phys. Chem., 15, 31 (1890). 

(2) Ann. Ghem. (Liebig), Suppl., 7, 354 (1870). 



W. Taylor measured the viscosity of one, two and 
three molar solutions of potassitun chloride, broniae and 
iodide in water at different temperatures and noted that 
negative viscosity may pass over into positive viscosity 
with rise in temperature and confirmed the view that vis- 
cosity depends upon the nature of both cation and anion. 
He noted also the negative viscosity effect of ammonium 
iodide when dissolved in v/ater. 

Eeference should be made to the extensive work of 

2 
Walden on the relations that exist between viscosity 

and conductivity at infinite dilutions. He finds that 

y^c^cy^,^ - for more than thirty organic solvents. 
Exceptions have been noted to this relationship and these 
will be taken up later . 

Glycerol as a solvent.- An examination of the litera- 
ture bearing on this problem shows that only a little work 

had been done previous to that of Jones and Schmidt. 

3 
Gattaneo measured the conductivity of several ha- 

lides of the metals in glycerol and noted that the values 

obtained were much smaller than the corresponding values 

in water or alcohol. 

(1) Edin Proc. 25, 227 (1904) and Edin Trans 45, 397 (1906 

(2) Zeit. f. Phys. Ghem. 78, 257 (1911). 

(3) Rend. E. Accad . Lincei., (5) 2, II, 112 (1893). 



1 

Schottner measured the viscosity of certain mix- 

2 
tures of glycerol and rater. Arrhenius studied the vis- 
cosity of mixtures of various organic substances with 
water, among them glycerol, and noted that the temperature 
coefficients of viscosity were greatest where the viscosity 

was greatest. 

3 

Schall and Van Rijn determined the relative vis- 
cosities of mixtures of glycerol with water and alcohol. 

4 
Lemke carried out an investigation on the conduc- 
tivity and viscosity of water glycerol mixtures at 25° 
and was led to conclude that ionization and hence elec- 
trical conductivity is proportional to the viscosity of 
the solvent as well as to the association. He noted the 
periodic viscosity of sodium chloride in 9.8 percent 
glycerol and water and a negative viscosity in water at 

certain dilutions. 

5 
Getman studied the viscosity of potassium iodide 

in various organic solvents including glycerol and noted 

negative viscosity only in the case of the latter. This 

he attributed to the association of the solvent. 

Jones and Schmidt have studied the conductivity 

of lithium bromide, cobalt chloride and potassium iodide 



(1) Wien. Ber. 77, II. 682 (1878). 

(2) Z. f. Phys. Chem. I, 285 (1887). 

(3) Ibid 23, 329 (1897). 

(4) Zeit. f. Phys. Chem. 52, 479 (1905) 

(5) J. Amer. Chem. Soc. 30, 1077 (1908) 

(6) Loc. cit. 



in glycerol at 25°, 35° and 45°, and in mixtures of 
gljj-cerol with water with ethyl alcohol anfl with methyl 
alcohol at 25° and 35°. Measurements of viscosity were 
also made with the N/lO solution in the various solvents. 
They have shown that glycerol is an excellent solvent and 
in all probability a comparatively good dissociant since 
it has a dielectric constant of 16.5 at 18° and an associa- 
tion factor of 1.8 at that temperature. From this data 

1 2 
glycerol accorciing to the Thompson, Nemst and Dutoit 

and Aston ^ hypothesis should h^ve a dissociating power 
close to that of ethyl alcohol. The extremely low con- 
ductivity values obtained were attributed to the high 
viscosity of the solvent. 

Schmidt noted that all the salts studied increased 
the viscosity of glycerol in K/lO solutions but that KI 
lowered the viscosity of water, and of 25 and 50 percent 
glycerol with water at 25° and 35°. He also shov.-ed that 
the effect of the several salts studied on the viscosity 
of glycerol was in inverse ratio to the atomic volume of 
the cations exactly analogous to the observations of Jones 
and Veazey in aqueous solutions. Schmidt also found 
glycerol to be an apparent exception to the observations of 
Walden, previously mentioned, that ^c^V,^ = C. Further 

(1) Phil. Ifeg. 36, 320 (1893). 

(2) Zeit. f. Phys. Ohem. 13, 531 (1894). 

(3) Conpt. Rend. 125, 240 (1897). 

(4) Zeits. f. Phys. Chem. 55, 246ff (1906) and 78, 257 (1911). 



exceptions in the case of water and glycol have been noted 
by 7/alden from his ototi investigations. 

The most extensive investigation of glycerol as a 
solvent has recently been carried out by Jones and Guy. 
They took up the behavior of seme tv^enty electrolytes in 
pure glycerol and in binary mixtures of glycerol with ethyl 
alcohol, with methyl alcohol and v/ith water at intervals 
of ten degrees from 25° to 75° for the pure solvent and 
from 25° to 45° in mixed solvents. Conductivity measure- 
ments were made over a range of V - 10 to Y = 1600 and 
viscosity measurements with the h/IO solutions. They find 
that the molecular conductivities in glycerol are all ex- 
tremely small but show a regular increase with increased 
dilution and rise in temperature. Furthermore a study 
of the temperature coefficients brought out the fact that 
in the case of those salts that have been shown to have 
large hydrating power in water, such as salts of barium 
strontium, calcium and cobalt, the relative increase was 
larger than v/ith salts of sodium potassium and ammonium 
which show little or no hydrating power in aqueous solu- 
tions. Here we have evidence of solvation in glycerol sup- 

2 
porting that obtained by Jones and Strong from spectro- 
scopic methods. 

In mixed solvents, Jones and Guy studied salts of 



(1) Amer. Chem. J., 46, 131 (1911). 

(2) Monographs Kos. 130 and 160, Carnegie Institution of 
Washington. 



8 



potassium, sodium, ammonium and strontium in various mix- 
tures of glycerol with water and with ethyl and methyl al- 
cohols. They find that conductivities in such mixtures do 
not follOT/ the law of averages but are always lower. This 
they explain by the facts established by Jones and Murray 
and Jones and Lindsay that two highly associated solvents 
when mixed tend to break down the association each of the 
other and hence their combined power of dissociating elec- 
trolytes is less than if there v;ere no mutual lowering of 
their association, i.e., if each solvent acted independent- 
ly of the other . 

From the viscosity data Guy has shown that the tem- 
perature coefficients of fluidity in pure glycerol are very 
large and nearly equal to those of conductivity. Also that 
the ternary electrolytes studied increased the viscosity 
of glycerol to a much greater extent than the binary elec- 
trolytes. This is attributed to the smaller atomic vol- 
umes of barium, strontium, calcium and cobalt and to the 
solvation of the molecules of the solute. In mixed sol- 
vents the curves representing connuctivity and fluidity 
were found to be strikingly analogous . 

Probably the most interesting point brought out by 
Guy was the large viscosity lowering observed in the case 

(1) Amer. Ghem. J., 30, 193 (1903). 

(2) Ibid 28, 3£9, 1902. 



1PZ iai 



of certain salts in pure glycerol, e.g., N/10 solutions of 
sodium nitrate, annonium bromide, amnoniun iodide and 
rubiflium bromide. The expl^^^'^ion of this phenomena is 
derived from that of Jones and Veazey for similar salts 
in water. This fact suggested the closer study of some 
of these sails over a wider range of concentration, the 
present investigation being a continuation of the v;ork of 
Jones and Schmidt and Jones and Guy. 



Work on this problem was begun in collaboration with 
Wm. A. A. Reinhardt, A.B., of Baltimore, a graduate of 
this university, whose untimely and lamentable death in 
September of last year prover^ a serious set back to the 
carrying out of the investigation. The writer wishes to 
pay tribute here to his friend and coworker as an earnest, 
sincere student, one who was rapidly coming to the front 
among the research students in this laboratory. 

The conductivity data on ammonium iodide in mixed 
solvents obtained by Mr. Reinhardt are incorporated in 
this paper. 



(l)Loo. Cit. 



10 



BXPERIMEIJTAL. 

Apparatus . 

The constant temperature baths used in this investi- 
gation were of the form usually employed for suoh work in 
this laboratory. The thermostat for viscosity measurements 
was provided with glass windows, both front and rear, to fa- 
cilitate the reading of the viscosimeters . Both baths were 
equipped with cooling coils in which the water was main- 
tained at constant pressure. This facilitated temperature 
regulation below 35°. A closely fitting cover was provid- 
ed for the conductivity bath for work above 35°, to pre- 
vent steaming and to maintain the air immediately above 
the cells at as near as possible the temperature of the 
water in the bath. 

The temperature of the thermostats was maintained con- 
stant to within 0.02° by means of electrically controlled 
gas regulators devised by Eeid . The thermometer used in 
the conductivity bath was of the usiial 100° enclosed 
scale type, graduated in 0.1 and could be read to .02° 
with a hand lens. For work up to 45° the viscosity bath 
was provided with a 25° Beclimann thermometer graduated to 
0.05° and with a certified Bender and Hobein thermometer 
for higher temperatures. All thermorreters v:ere first 
standardized against a certified Reichsanstalt instrument 

(1) Amer. Chem. J., 41, 148 (1909). 



and comparisons were frequently made during the course of 
the work. 

The conductivity apparatus consisted of the usual 
Kohlrausch slide wire hridge, resistance box, inequation 
coil and telephone receiver. This apparatus was made and 
standardized by Leeds and Northrup of Philadelphia and in 
addition the resistances were compared with a rheostat 
which had been standardized by the Bureaii of Standards, 
Washington, D.G. The bridge wire was calibrated as direct- 
ed by Jones and found to be of uniform resistance thru- 
out. Under favorable conditions separate readings with the 
same resistance agreed with one another to one half of a 
millimeter, the nature of the solvent preventing closer 
agreements . 

The conductivity cells used were of two types, those of 

2 
the ordinary plate type as described by Bingham, had con- 
stants ranging from 40 to 339 and were used v;ith the more 
concentrated solutions. For the K/10 to h/1600 solutions, 

five cells of the type previously described by Jones and 

3 4 

Schmidt, and Jones and Kreider were used. Their constants 

ranged from S.35 to 4.36, and because of this they were well 

adapted to the measurement of high resistances. 

(1) Freezing Point Boiling-point and Conductivity Methods. 

(2) Loc. Git. 

(3) Loc. cit. 

(4) Loc. cit. 



12 



Cell constants were determined with a fiftieth normal 
potassium chloride solution as a basis, this being diluted 
to five -hundredth and two -thousandth normal for the lov; 
constant cells. Checks were made at regular intervals and 
showed only slight variations in the cell constants, especial- 
ly in the case of the cells with concentric cylindrical 
electrodes. 

The molecular conductivity of the fiftieth normal so- 
lution was taken as 129.7 reciprocal Siemens units, at 25°. 
That of the more dilute solutions was determined by direct 
measurements . 

Viscosity measurements were made with the Ostwald 

1 2 

viscosimeter as modifier! by Jones and Veazey, the sise 

of the capillary being regulated to the solutions for which 
they were employed. The viscosimeters were calibrated as 
described by Schmidt, the time of flow for water in the 
instruments used for glycerol being derived from the 
formula: ^^^ ./ /// 

where j^^ is the time of flow of water in the water vis- 

_,/ 
cosimeter, 7^ the time for a slightly more viscous solution 

,// /// A-*' 
in the water viscosimeter; -f , t and 7^ the times of 



(1) Ostwald-Luthor: Phys.-chem. Mess. 3rd Sd. (1910), 
p. 232. 



(2) Zeit. f. Phys. Chera. 61, 641 (1908). 

(3) Loc. eit. 



13 



flow of the solutions A and B of intermediate viscosities 
between water and glycerol in an intermediate viscosimeter 
and in the instrument for glycerol; t^ the derived time of 
flow in the glycerol viscosimeter. The viscosineters were 
filled by means of carefully calibrated pipettes with such 
a volume of liquid as to fill them from the middle of the 
upper to the middle of the lower bulb. With such an ar- 
rangement, according to Appleby ^ the alteration in hydro- 
static pressure due to small variations in the volume of 
the liquid is a minimum. 

On account of the steaming of the viscosity thermostat 
at high temperatures, the viscosineters after filling were 
provided with a simple apparatus designed to exclude dust 
and moisture and to eliminate the danger of obstructing 
the free passage of the air from one arm of the viscosimeter 
to the other during the flow of the liquid through the capil- 
lary. This consisted of two T shaped guard tubes each pro- 
vided with a small bulb in the long ann. These bulbs -.vere 
filled with cotton vrool to filter out dust particles. One 
end of the cross arm of a guard tube was connected to each 
arm of the viscosimeter and the opposite ends joined by a 
short length of rubber tubing. The liquid was drawn up in 
the capillary arm of the viscosimeter by compressing the 
rubber tube and attaching the bulb arm of the guard tube 
on that side to an aspirator, the air entering through the 
guard tube on the opposite (reservoir) arm is thoroughly 

(1) J. Chem. Soc, 972, SOOO (1910). 



14 



dried "by passing over calcium chloride and freed from dust 
ty the cotton wool mentioned above. When the liquid has 
risen to a point slightly above the upper mark on the vis- 
cosimeter the compression on the rubber tube is released 
and the air pressure immediately equalizes itself on both 
sides of the viscosimeter . By this arrangement no air from 
the outside enters during the actual flow of the liquid 
through the capillary. 

Viscosimeter s, while being read, were supported in 
the bath by means of special clamps with cork lined jaws 
attached to a heavy stand which was carefully leveled. 

Specific gravity determinations were made by means 
of the Ostwald pycnometer as modified for liquids with 
large expansion by Jones and Veazey. 

All measuring flasks and pipettes were carefully cali- 
brated either by direct weighing or by the method of Morse 

2 
and Blalock to hold aliquot parts of the true liter at 

20°, and solutions were brought to v;ithin<9.1° of this 

temperature before being diluted to the mark. 

Solutions . 
Because of a limited supply of salts at hand all solu- 
tions were made up at 20° and a temperature correction made 

(1) Loc. Git. 

(2) Amer. Chem. J., 16, 479 (1904). 



15 



for temperatui'es above 25°. The expansion coefficient for 
glycerol was taken as .00049 and was determined from speci- 
fic gravity measurements in the viscosity work. 

Solutions of the N, 3/4 N, n/2, 11/4 and l/lO normal 
were made by direct weighing of the anhydrous salt which 
had been previously dried for some time in an air bath at 
130°-1353.From the l/lO normal solution the K/50 and K/lOO 
solutions were made by dilution. These in turn served as 

* 

mother solutions for the M/200 and 11/400 from which the 
U/eOO and K/1500 solutions were made in a similar manner. 
The latter was made by diluting the H/400 solution four 
times. 

Because of the hydroscopic nature of the solvent and 
the difficulty in obtaining proper drainage of burettes 
containing it, measuring flasks were used exclusively in 
the dilution of solutions in glycerol. In every case the 
proper measuring flask was filled with the mother solution, 
set in a thermostat at 20°, warmed in an air bath to 70°-80°, 
drained as quickly as possible with the receiving flask, 
then washed out at least three times with the warmed sol- 
vent. The flask containing the more dilute solution was 
then filled up nearly to the neck with the solvent warmed 
and shaken thoroughly without wetting the neck, then filled 
to a point slightly above the nark and finally set after 
cooling to 20° in a thermostat. Final warming in the air 
bath and thorough shaking completed the operation. The 
flasks used were of Jena Eormal glass, eliminating as far 



as possible the danger of the action of the solvent on the 
glass. Some time was allowed before the final dilution to 
the nark to permit tho glass to contract properly after the 
unavoidable heating during the process of dilution. 

On account of the extremely high resistance offered 
^y glycerol solutions conductivity measurements were not 
made at dilutions greater than U/l600. Even at that dilu- 
tion considerable difficulty was experienced in obtaining 
concordant readings. As an example it might be well to 
note that I\f/1600 solutions in glycerol in a cell with a 
constant as low as 2.3 required a balancing resistance of 
from 8,000 to 10,000 ohms while pure glycerol in the same 
cell required 20,000 to 22,000 ohms. 

Confluotivity ancf viscosity measurements in pure 
glycerol were made at intervals of ten degrees from 20° 
to 75° and jn glycerol-watcr mixtures at 25 , 35°, and 
45°. Viscosity measurements were not made at a greater 
dilution than K/10 since at lower concentrations ^ ap- 
proaches yjc^ too closely to be accurately differentiated. 

Solvents . 
Glycerol . - The glycerol used was from a new lot of 
Kahlbaum's "Doppelt - Dist. 1.26" and had a mean specific 
conductivity of about 0.6 x 10"*^ at 25° and a mean specific 
gravity of 1.257 at the same temperature. Ho attempt was 
made to redistill it, since Schmidt had already shown that 
redistillation clid not appreciably lower the conductivity. 



17 



Water . - The water was purified by the rnethod of 

Jones and Mackay with the improyement as mentioned by 

2 

Schmidt and had a mean specific confluctivity of 1.5-2 x 

-G o 

10 at 25". 



Salts . 
The Eubidium and Ammonium salts used in this work 
were from Kahlbaum's best products. These were re crystal- 
lized two or three times from conductivity water and care- 
fully dried each time at 130-135° before weighing. In 
addition the rubidium salts were examined spectroscopical- 
ly and showed the presence of only traces of sodium and no 
potassium. The ammonium iodide was ptire white after dry- 
ing and solutions of it in glycerol were only slightly 
tinted after standing some time. 

Procedure. 



Conductivity data was calculated in the usual way. 
Viscosity measurements were calculated fron the 
formula 

ri^ Set 

in v;hich is the viscosity coefficient for the liquid 
in question, the absolute viscosity of water, S the 
specific gravity of the liquid at the given temperature, 

(1) Amer. Chem. J. 1783 (1895). 

(2) loc. Git. 



J.O 



t the time of flow of the same, Sq and to the density 
and time of flow of water at the same temperature. 
Fluidity was calculated from the formula 

<f>-' f- 

where (p represents the fluidity. 

The absolute viscosities of water as driven by 

Thorpe and Roger are 

25° 0.00891 55° 0.005055 

350 0.00720 65° 0.C04355 

45° 0.00597 75° 0.003795 

Temperature coefficients. - The temperature coeffi- 
cients in conductivity units represent simply the actual 
increase in conductivity per degree rise in temperature. 

Percent, temperature coefficients, both of conductivi- 
ty and fluidity, were calculated from the formula 

Temp, ooeff. of lA,,f]. ~J— . (5fe.#£H^^.^k£ " 

An attempt was made to obtain conductivity and vis- 
cosity data on the sulfate of rubidium^ but it was not pos- 
sible to obtain a solution of higher concentration than 
Ij/200. 

It was originally intended to carry on a parallel 
investigation with caesium salts, but we have been thus far 
unable to secure sufficient quantities for the work. 

(1) Loc. Git. 



19 



TABLE I . - Molecular Conductivity of Ammonium lodicie in 
Glycerol at £5°, 35°, 45°. 



A 25O 



/fy 35 < 



>^450 



1. 


,0 


0.389 


0.770 


1.385 


1. 


,3 


0.371 


0.746 


1.361 


2. 


,0 


0.348 


0.717 


1.312 


4. 


,0 


0.326 


0.665 


1.224 


10 




0.342 


0.700 


1.321 


50 




0.359 


0.740 


1.373 


100 




0.369 


0.764 


1.414 


200 




0.365 


0.760 


1.396 


400 




0.371 


0.753 


1.401 


800 




0.404 


0.777 


1.441 


1600 




0.413 


0.811 


1.457 



TABLE 


II. - 


Temperature Coefficients. 


Cond. 


Units. 


V 




Per Cent. 








250-35° 350-45° 


250-35° 


35O-45O 


1 




0.0979 0.0799 


0.0381 


0.0615 


1. 


3 


0.1012 0.0824 


0.0375 


0.0615 


2 




0.1060 0.0830 


0.0369 


0.0595 


4 




0.1040 0.0841 


0.0339 


0.0559 


10 




0.1047 0.0887 


0.0358 


0.0621 


50 




0.1061 0.0855 


0.0381 


0.0633 


100 




0.1070 0.0851 


0.0395 


0.0650 


200 




0.1082 0.0837 


0.0395 


0.0636 


400 




0.1030 0.0860 


0.0382 


0.0648 


800 




0.0923 0.0854 


0.0373 


0.0664 


1600 




0.0964 0.0797 


0.0398 


0.0646 



20 



TABIE III. - Molecular Conduotlvlty of Aramonlum Iodide in 
Glycerol at 55°, 65°, 75°. 



A 55* 



1, 


.0 


2.304 


1. 


,3 


2.268 


2. 


,0 


2.140 


4. 


.0 


2.069 


10 




2.210 


50 




2.331 


100 




2.424 


200 




2.386 


400 




2.410 


800 




2.485 


1600 




2.528 



>/ 650 



>^V50 



3.602 


5.260 


3.540 


5.189 


3.404 


5.07 2 


3.266 


4.858 


3.506 


5.278 


3.707 


5.534 


3.843 


5.772 


3.805 


5.606 


3.819 


5.749 


4.010 


5.950 


4.130 


6.100 



TABLE IV. - Temperature Coefficients 







Per Cent . 






Cond. 


Units. 


V 


45^-55° 


550-65° 


65°-750 


45°-55° 


55°-65° 


' 650-75° 


1 


0.0663 


0.0563 


0.0460 


0.0919 


0.1298 


0.1658 


1.3 


0.0666 


0.0561 


0.0466 


0.0907 


0.1272 


0.1649 


2 


0.0631 


0.0591 


0.0490 


0.0828 


0.1264 


0.1668 


4 


0.0690 


0.0578 


0.0487 


0.0845 


0.1197 


0.1592 


10 


0.0673 


0.0586 


0.0505 


0.0889 


0.1296 


0.1772 


50 


0.0698 


0.0590 


0.0493 


0.0958 


0.1376 


0.1827 


100 


0.0714 


0.0585 


0.0476 


0.1010 


0.1419 


0.1829 


200 


0.0709 


0.0590 


0.0473 


0.0990 


0.1419 


0.1801 


400 


0.0720 


0.0585 


0.0505 


0.1009 


0.1409 


0.1930 


800 


0.0724 


0.0614 


0.0484 


0.1044 


0.1525 


0.1940 


,600 


0.0735 


0.0634 


0.0477 


0.1071 


0.1602 


0.1970 



21 



TABI*E V. - Molecular Conductivity of Rubidium Chloride 
in Glycerol at 25^^, 55° . 45° . 



A 25^ 



1. 


0.374 


1.3 


0.371 


2 


0.386 


4 


0.376 


10 


0.380 


50 


0.401 


100 


0.420 


200 


0.428 


400 


0.432 


800 


0.444 


1600 


0.448 



Af^ 35° 



>^ 45° 



0.738 


1.320 


0.740 


1.337 


0.767 


1.371- 


0.771 


1.390 


0.771 


1.410 


0.819 


1.502 


0.848 


1.563 


0.860 


1.588 


0.887 


1.633 


0.874 


1.625 


0.892 


1.643 



TABLE VI. - 


Temperature 


Coefficients 


• 






Per 


Cent. 


Cond . 


Units. 


V 


25°-35° 


35°-45° 


25°-35° 


35° -45' 


1. 


0.0973 


0.0789 


0.0364 


0.0582 


1.3 


0.0995 


0.0807 


0.0369 


0.0597 


2. 


0.0987 


0.0812 


0.0381 


0.0623 


4 


0.1050 


0.0784 


0.0395 


0.0604 


10 


0.1029 


0.0829 


0.0391 


0.0639 


50 


0.1042 


0.0834 


0.0418 


0.0683 


100 


0.1019 


0.0843 


. 0428 


0.0715 


200 


0.1009 


0.0846 


0.0432 


0.0728 


400 


0.1053 


0.0841 


0.0455 


0.0746 


800 


0.0970 


0.0859 


0.0430 


0.0751 


1600 


0.0991 


0.0842 


0.0444 


0.0751 



22 



TABLE VII. - Molecular Gonductivlty of Rubidium Chloride 
in Glyoerol at 55^, 65f^, 75° - 



1. 

1.3 

2 

4 

10 

50 

100 

200 

400 

800 

1600 



.//. 55^ 



y^. 65^ 



>. 



75* 



2.205 


3.400 


4.994 


2.215 


3.421 


5.014 


2.307 


3.570 


5.272 


2.310 


3.585 


5.382 


2.386 


3.749 


5.684 


2.561 


4.003 


6.041 


2.649 


4.180 


6.343 


2.720 


4.282 


6.408 


2.784 


4.408 


6.542 


2.774 


4.358 


6.532 


2.831 


4.462 


6.574 



TABTiF. VIII. 


Temperature Coe 


ffioients 


• 








Per 


Cent . 




Cond. 


Units . 


V 


45°-550 


55^-65° 


65°-750 


45°-55° 


55°-650 


65°-75° 


1. 


0.0670 


0.0542 


0.0469 


0.0885 


C.1195 


0.1594 


1.3 


0.0657 


0.0544 


0.0466 


0.0878 


0.1206 


0.1593 


2 


0.0677 


0.0547 


0.0477 


0.0936 


0.1253 


0.1702 


4 


0.0662 


0.0553 


0.0501 


0.0920 


0.1275 


0.17 97 


10 


0.0692 


0.0571 


0.0516 


0.0976 


0.1363 


0.1935 


50 


0.0705 


0.0563 


0.0509 


0.1059 


. 1442 


0.2038 


100 


0.0695 


0.0578 


0.0517 


0.1086 


0.1531 


0.2163 


200 


0.0713 


0.0574 


0.0496 


0.1132 


0.1562 


0.2126 


400 


0.0705 


C.0547 


0.0484 


0.1151 


0.1524 


0.2134 


800 


C.0707 


0.0571 


0.0498 


0.1149 


0.1584 


0.2174 


1600 


0.0723 


0.0576 


0.0473 


0.1188 


0.1631 


0.2112 



23 



TABLE rx. - 



Mol.ecular Conductivity of Rubidium Bromide 
in Glyoerol at 25°, 35°, 45°. 



1. 

1. 

4 

10 

50 

100 

200 

400 

800 

1600 



yl/^ 25° 



>^ 35° 



y^^ 450 



0.368 


0.717 


1.273 


0.360 


.716 


1.311 


0.363 


0.73E 


1.339 


0.369 


0.752 


1.385 


0.379 


0.785 


1.456 


0.409 


0.835 


1.483 


0.427 


0.855 


1.592 


0.451 


0.879 


1.627 


0.470 


0.893 


1.633 


0.480 


0.932 


1.700 



TABT,^ 


X. - 


Temperature Coefficients 


• 








Per 


Cent . 


Cond. 


Units. 


V 


25°-35° 


35°-45° 


25°-35° 


35°-450 


1. 




0.0948 


0.0775 


0.0349 


0.0556 


1. 


3 


0.0989 


0.0831 


0.0356 


0.0595 


4 




0.1016 


0.0828 


0.0369 


0.0607 


10 




0.1037 


0.0842 


0.0383 


0.0633 


50 




0.1071 


0.0855 


0.0406 


0.0671 


100 




0.1057 


0.0776 


0.0429 


0.0648 


200 




0.1036 


0.0862 


0.0435 


0.0737 


400 




0.1011 


0.0851 


0.0442 


0.0748 


800 




0.1020 


0.0829 


0.0451 


0.0740 


1600 




0.1198 


0.0824 


0.0508 


0.0768 



TABLE XI. - Mole on la r GonductiT-ity of P.ubidiurn 3romlde 
in Glycerol ajt 55° . 65°. 750 . 



x4 55' 



1. 


2.143 


1.3 


2.198 


4 


2.217 


10 


2.324 


50 


2.473 


100 


2.623 


200 


2-698 


400 


2.711 


800 


2.7E4 


1600 


2.722 



/^K 



65^ 



3.056 
3.424 
3.489 
3.676 
3.876 
4.153 
.291 
.348 
,401 
.499 



4. 
4. 

4, 
4, 



^. "75° 



4.595 
4.604 
5.120 
5.483 
763 
236 
477 
592 
666 



5. 
6, 
6, 
6. 
6 



6.855 



TABLE XII. - Temperature Coefficients. 







Per 


Cent. 




Cond. Units. 


▼ 


45°-55° 


55°-65° 


65°-75° 


45°-55Q 


55°-65° 


650-750 


1. 


0.0683 


0.0426 


0.0504 


0.0870 


0.0913 


0.1539 


1.3 


0.0677 


0.0558 


0.0345 


0.0887 


0.1225 


0.1180 


4 


0.0656 


0.0569 


0.0318 


0.0878 


0.1262 


0.1631 


10 


0.0678 


0.0580 


0.0492 


0.0939 


0.1352 


0.1807 


50 


0.0698 


0.0567 


0.0487 


0.1017 


0.1402 


0.1887 


100 


0.0769 


0.0583 


0.0501 


0.1140 


0.1530 


0.2083 


200 


0.0693 


0.0590 


0.0509 


0.1104 


0.1593 


0.2186 


400 


0.0650 


0.0604 


0.0516 


0.1058 


0.1637 


0.2244 


800 


0.0668 


0.0616 


0.0515 


0.1091 


0.1677 


0.2265 


1600 


0.0601 


0.0653 


0.0524 


0.1022 


0.1777 


0.2356 



TABLE ZIII. - Moleoular Conductivity of Rubidium Iodide 
in Glycerol at 25°, 35°, 45°. 



V 


Jf, 25° 


1. 


0.355 


1.33 


0.342 


2 


0.334 


4 


0.321 


10 


0.323 


50 


0.345 


100 


0.356 


200 


0.363 


400 


0.368 


800 


0.370 


600 


0.373 



yU^ 35° 

0.704 
0.688 
0.680 
0.649 
0.657 
0.703 
0.721 
0.745 
0.751 
0.781 
0.805 



^4- 45° 

1.275 
1.252 
1.236 
1.212 
1.213 
1.330 
1.361 
1.373 
1.391 
1.380 
1.389 



TABLE XIY. - 


Temperature 


Coefficients. 








Per Gent. 


Cond . 


Units. 


V 


25°-350 


35°-450 


25°-35° 


35°-450 


1. 


0.0983 


0.0810 


0.0349 


0.0571 


1.33 


0.1012 


0.0819 


0.0346 


0.0564 


2. 


0.1036 


0.0818 


0.0346 


0.0556 


4 


0.1022 


0.0867 


0.0328 


0.0563 


10 


0.1034 


0.0846 


0.0334 


0.0556 


50 


0.1038 


0.0892 


0.0358 


0.0627 


100 


0.1025 


0.0888 


0.0365 


0.0640 


200 


0.1052 


0.0844 


0.0382 


0.0628 


400 


0.1041 


0.0857 


0.0383 


0.0644 


800 


0.1110 


0.0767 


0.0411 


0.0599 


1600 


0.0159 


0.0725 


0.0432 


0.0584 



26 



TABLE XV.- Molecular Gonduetivlty of RuTDldlum Iodide 
in Glycerol at 55° . 65°. 75°. 



X/ 55° 



1. 


2.111 


1.3 


2.100 


2. 


2.089 


4. 


2.034 


10 


2.007 


50 


2.256 


100 


2.320 


200 


2.360 


400 


2.408 


800 


2.405 


1600 


2.395 



>^ 65° 



y^. 75' 



3.229 


4.771 


3.286 


4.812 


3.278 


4.829 


3.197 


4.703 


3.103 


4.667 


3.575 


5.408 


3.687 


5.466 


3.861 


5.743 


3.937 


5.832 


3.941 


5.756 


4.150 


5.809 



TABLE rVI. - Tem-Derature Coefficients. 







Per Cent 


• 




Cond. Uni 


ts. 


V 


45°-55° 


55°-65° 


65°.75° 


45°-55° 


55°-65° 


65°.75<> 


1. 


0.0656 


0.0530 


0.0474 


0.0836 


0.1118 


0.1542 


1.3 


0.0677 


0.0565 


0.0464 


0.0848 


0.1186 


0.1526 


2. 


0.0690 


0.0569 


0.0473 


0.0853 


0.1189 


0.1551 


4. 


0.0678 


0.0572 


0.0471 


0.0822 


0.1163 


0.1506 


10 


0.0674 


0.0546 


0.0499 


0.0794 


0.1096 


0.1564 


50 


0.0696 


0.0584 


0.0541 


0.0926 


0.1318 


0.1833 


100 


0.0705 


0.0588 


0.0455 


0.0960 


0.1366 


0.1779 


200 


0.0719 


0.0636 


0.0487 


0.0967 


0.1501 


0.1882 


400 


0.0731 


0.0635 


0.0481 


0.1017 


0.1529 


0.1895 


800 


0.0742 


0.0628 


0.0461 


0.1025 


0.1536 


0.1815 


1600 


0.0724 


0.0732 


0.0402 


0.1006 


0.1755 


0.1659 



TABLE XVII. - Moleoular Gonduotivlty of R ubiflium Nitrate 
in Glyoerol at 25£, 55° . 45°. 



Jf. 25' 



/^^ 35' 



2 


0.299 


0.625 


4 


0.294 


0.611 


10 


0.325 


0.666 


50 


0.366 


0.742 


100 


0.386 


0.793 


200 


0.388 


0.793 


400 


0.407 


0.801 


800 


0.417 


0.873 



>. 45° 



1.093 
1.127 
1.228 
1.384 
1.450 
1.490 
1.471 
1.550 



TABLE ZVIII. - Temperature Qoeffieients 



'C^ 





Per 


Cent. 


Gond. 


Units. 


V 


25°-35° 


350-45° 


25°-35° 


35° -450 


2 


0.1090 


0.0749 


0.0326 


0.0468 


4 


0.1078 


0.0844 


0.0317 


0.0516 


10 


0.1046 


0.0844 


0.0341 


0.0562 


50 


0.1027 


0.0855 


0.0376 


0.0642 


100 


0.1051 


0.0829 


0.0407 


0.0657 


200 


0.1044 


0.0879 


0.0405 


0.0697 


400 


0.0968 


0.0836 


0.0394 


0.0670 


800 


0.1096 


0.0776 


0.0456 


0.0677 



TABLE XIX. - Molecular G opduGtlvity of Rubiaium Hltrate 
in Glycerol at 55_^, 65^, 75^ . 



28 



2 

4 
10 

50 

100 
200 
400 
800 



^. 550 



/^ 65* 



^.75° 



1.930 


3.005 


4.435 


1.913 


2.97 9 


4.392 


2.088 


3.272 


4.866 


2.350 


3.712 


5.570 


2.481 


3.917 


5.894 


2.495 


4.000 


5.960 


2.487 


3.932 


5.862 


2.605 


4.161 


6.174 



TABLE XX. - Temper a t-ure Coefficients 







Per Cent. 




Cond. 


Units. 




▼ 


45°-550 


550-65° 


65O-75O 


45°-55° 


55O-65O 


650-75 


2 


0.0763 


0.0557 


0.0475 


0.0837 


0.1075 


0.1430 


4 


0.0698 


0.0557 


0.0474 


0.0786 


0.1066 


0.1413 


10 


0.0700 


0.0568 


. 0487 


0.0860 


0.1184 


0.1594 


50 


0.0699 


0.0579 


0.0505 


0.0966 


0.1362 


0.1858 


100 


0.0710 


0.0579 


0.0505 


0.1031 


0.1436 


0.1977 


200 


0.0674 


0.0602 


0.0491 


0.1005 


0.1505 


0.1963 


400 


0.0690 


0.0581 


0.0491 


0.1016 


0.1445 


0.1930 


800 


0.0680 


0.0597 


0.0483 


0.1055 


0.1556 


0.2013 



TABLE XXI. - Molecular Conduotivlty of Acmon lum lodlcle in a 
Mixture of 75 percent Glycerol with Water at 
25°, 350 . 45°. 



J/^ 25 



^ 350 



>^ 450 



1.0 
1.3 
2.0 
4.0 
10 
50 
100 
200 
400 
800 
1600 



5.48 
5.39 
5.24 
5.18 
5.26 
5.56 
5.71 
5.81 
5.76 
6.06 
6.03 



8.24 


11.61 


8.11 


11.53 


8.00 


11.50 


7.99 


11.47 


8.16 


11.75 


8.64 


12.56 


8.89 


12.94 


9.05 


13.19 


8.99 


13.18 


9.44 


13.74 


9.39 


13.73 



TABIE XXII. - Temperature Coefficients. 





Per 


Cent. 


Cond. 


Units. 


V 


25°-350 


35°-450 


25O-35O 


35°-45° 


1.0 


0.0504 


0.0409 


0.276 


0.337 


1.3 


0.0505 


0.0422 


0.272 


0.342 


2.0 


0.0527 


0.0437 


0.276 


0.350 


4.0 


0.0542 


0.0435 


0.281 


0.348 


10 


0.0551 


0.0440 


0.290 


0.359 


50 


0.0572 


0.0454 


0.318 


0.392 


100 


0.0557 


0.0456 


0.318 


0.405 


200 


0.0558 


0.0457 


0.324 


0.414 


400 


0.0561 


0.0466 


0.323 


0.419 


800 


0.0560 


0.0456 


0.339 


0.430 


1600 


0.0557 


0.0462 


0.336 


0.434 



30 



TABLE XXIII. - Moleoular Oonduetlvlty of Ammon lura Iodide in 
a Mixture of 50 per oent Glyoerol with V/ater 
at 25^, 352, 45^. 



y^^ 25' 



>^ 35< 



1. 





22.38 


1. 


3 


22.19 


2. 





22.12 


10 




23.15 


50 




24.69 


100 




25.52 


200 




25.49 


400 




25.68 


800 




26.29 


1600 




26.62 



29.40 
29.36 
29.51 
31.27 
33.40 
34.54 
34.66 
35.20 
35.87 
36.21 



^^ 45° 

37.24 
37.25 
37.55 
40.34 
43.16 
44.83 
45.18 
45.30 
46.18 
47.00 



TABLE XXIY. - Temperature Coeff ioients 







Per 


Cent . 


V 




250-35Q 


35°-45° 


1. 





. 03 14 


0.0267 


1. 


3 


0.0323 


0.0269 


2. 





0.0334 


0.027E 


10 




0.0351 


0.0290 


50 




0.0353 


0.0292 


100 




0.0353 


0.0301 


200 




0.0360 


0.0303 


400 




0.0371 


0.0287 


800 




0.0364 


0.0287 


1600 




0.0360 


0.0298 



Cond . 


Units. 


25°-350 


35°-45° 


0.702 


0.784 


0.717 


0.789 


0.739 


0.804 


0.812 


0.907 


0.871 


0.976 


0.902 


1.029 


0.917 


1.052 


0.952 


1.010 


0.958 


1.031 


0.959 


1.079 



31 



TABLE XZV. - Molecular Conductivity of Ammonium Iodide in 
a Mixture of 25 per cent Glycerol with Water 
at 250, 35^, 450 . 



10 
50 
100 
200 
400 
800 
1600 



61.58 
64.32 
66.69 
68.54 
68.12 
69.21 
69.68 



y^^ 35^ 

76.71 
80.30 
82.86 
85.87 
85.07 
87.26 
88.47 



/^ 



450 



92.62 
98.25 
101.50 
104.39 
104.17 
105.92 
106.85 



TABLE XXV 1. - 


■ Temperature 


Coefficients 




Per 


Cent . 


V 


250-35° 


35°-450 


10 


0.0246 


0.0207 


50 


0.0248 


0.0223 


100 


0.0242 


0.0225 


200 


0.OE56 


0.0201 


400 


0.0249 


0.0224 


800 


0.0261 


0.0214 


1600 


0.0269 


0.0208 



Gond. 


Units. 


25°-350 


35O-450 


1.515 


1.591 


1.598 


1.795 


1.617 


1.864 


1.733 


1.852 


1.695 


1.910 


1.805 


1.866 


1.879 


1.838 



3£ 



TABLE XIVII.- Molecalar Conductivity of Ammonium Iodide 
in Water at 25° . 55^ . 45° , 



1.3 
2 

4 

10 

50 

100 

200 

400 

800 

1600 



J/^ 25° 

100.7 

102.5 
105.3 
121.3 
135.2 
136.3 
139.0 
143.1 
151.1 
154.7 



Jf, 35° 

114.1 
125.3 
125.8 
148.6 
160.5 
161.3 
168.5 
171.2 
182.0 
184.6 



y^^ 450 

130.4 
147.5 
151.3 
172.6 
186.3 
190.8 
197.7 
202.9 
215.1 
218.4 



TABLE iXVlll. 


- Temperati 


ire Goeffioie 


nts. 








Per 


Gent. 




Cond. 


Units. 


V 


25°-35° 


35°-45° 


25°-350 


35°-450 


1.3 


. 0133 


0.0143 


1.34 




1.63 


2 


0.0222 


0.0178 


2.28 




2.22 


4 


0.0195 


0.0202 


2.05 




2.55 


10 


0.0225 


0.0161 


2.73 




2.40 


50 


0.0187 


0.0160 


2.53 




2.58 


100 


0.0184 


0.0182 


•2.50 




2.95 


200 


0.0212 


0.0173 


2.95 




2.92 


400 


0.0196 


0.0185 


2.81 




3.17 


800 


0.0204 


0.0176 


3.09 




3.21 


.600 


0.0193 


0.0183 


2.99 




3.38 



TABIE XZIX. - Moleo-glar Conduotivity of Rubidinm Bromide 
in a Mixture of 75 per cent Glycerol with 
Water at 25f;, 35^, 45° . 



yt^u 25° 



1. 


5.33 


1.33 


5.31 


8 


5.39 


4 


5.43 


10 


5.67 


50 


6.15 


100 


6.27 


200 


6.35 


400 


6.41 


800 


6.52 


1600 


6.52 



7.81 
7.94 
8.05 
8.28 
8.63 
9.31 
9.67 
9.79 
9.87 
10.03 
10.07 



y^^ 



45° 

10.87 
11.07 
11.57 
11.79 
12.31 
13.46 
13.86 
14.11 
14.28 
14.45 
14.51 



TABLE 


J(XX. - 


Temperature Coefficients. 










Per Cent. 


Cond. 


Units . 


V 




25°-35° 350-45° 


250-35° 


35°-450 


1 




0.0465 0.0392 


0.248 


0.306 


1. 


33 


0.0495 0.0394 


0.263 


0.313 


2 




0.0494 0.0437 


0.266 


0.352 


4 




0.0525 0.0424 


0.285 


0.351 


10 




0.0522 0.0426 


0.296 


0.368 


50 




0.0514 0.0446 


0.316 


0.415 


100 




0.0542 0.0433 


0.340 


0.419 


200 




0.0542 0.0441 


0.344 


0.432 


400 




0.0540 0.0448 


0.346 


0.441 


800 




0.0538 0.0441 


0.351 


0.442 


1600 




0.0544 0.0441 


0.355 


0.444 



34 



TABLE XZZI. - Molecular Gonduotivlty of Hub id lug Bromide 
in a Mixture of 50 per cent Glycerol with 
Water at^ 25^, 55° . 45°. 



A. 25° 



1. 


21.65 


1.33 


21.38 


2 


22.31 


4 


23.33 


10 


24.51 


50 


26.25 


100 


26.87 


200 


27.54 


400 


27.97 


800 


28.47 


1600 


28.39 



27.98 
28.33 
28.90 
30.84 
32.73 
34.85 
36.02 
37.01 
37.47 
38.35 
38.33 



35 . 27 
36.37 
36.75 
39.31 
41.85 
44.92 
46.72 
48.17 
48.39 
49.60 
49.48 



TABLE XZXII.- Temperature Ooeff icients . 





Per 


Cent. 


Cond 


. Units. 


V 


25°-350 


350-45° 


25°-55° 


350-45° 


1 


0.0292 


0.0261 


0.633 


0.729 


1.33 


0.03^5 


0.0284 


0.695 


0.804 


2 


0.0295 


0.0280 


0.659 


0.785 


4 


0.0321 


0.0281 


0.751 


0.847 


10 


0.0335 


0.0279 


0.822 


0.912 


50 


0.0328 


0.0289 


0.860 


1.007 


100 


0.0340 


0.0297 


0.915 


1.070 


200 


0.0344 


0.0301 


0.947 


1.116 


400 


0.0340 


0.0292 


0.950 


1.092 


800 


0.0347 


0.0293 


0.988 


1.125 


1600 


0.0350 


0.0291 


0.994 


1.115 



35 



TABIE ZZZIII 



- Molecular Conduotivity of Rubidium Bromide 
in a Mixture of 25 per cent Glyoerol with 
Water at 25_^, 35^, 45*^ . 



2 
4 

10 
50 
100 
200 
400 
800 
1600 



^^ 25° 

51.79 
54.23 
62.88 
69.27 
69.44 
71.39 
73.40 
74.16 
82.85 



/4. 35° 

65.77 
67.23 
76.85 
84.84 
86.22 
89.09 
91.15 
92.10 
101.59 



y/^ 450 

79.87 
81.80 
93.67 
103.77 
105.46 
108 . 43 
111.22 
111.81 
123.19 



TABLF. XZZIV. - Temperature Goeff ioients , 



Per Gent . 



Cond. Units. 



25°-35' 



35°-450 



250-350 



350-450 



2 
4 

10 

50 
100 
200 
400 
800 
1600 



0.0270 


0.0214 


1.398 


1.410 


0.0240 


0.0217 


1.300 


1.457 


0.0222 


0.0219 


1.397 


1.682 


0.0225 


0.0223 


1.557 


1.893 


0.0239 


0.0223 


1.678 


1.924 


0.0248 


0.0217 


1.770 


1.934 


0.0242 


0.0220 


1.775 


2.007 


0.0242 


0.0214 


1.794 


1.971 


0.0226 


0.0213 


1.874 


2.160 



36 



TABLE XXXV. - Molecular Conductivity of Rubidium Bromide 
in Vfater at 25^, 35^, 45£. 



2 

4 

10 

50 

100 
200 
400 

800 
1600 



96.3 
107.8 
121.8 
137.2 
142. '2 
143 .3 
148.4 
152.8 
151.8 



y^^ 35° 

119.8 
132.1 
143.8 
163.0 
167.2 
170.1 
174.9 
179.1 
179.9 



^.- 45° 

137.4 
153.3 
165.8 
189.3 
195.4 
199.9 
202.2 
208.3 
211.7 



TABT.T?. ZXXVI. - 


Temperature Goefficiei 


its. 






Per 


Cent. 


Cond. 


Units. 


V 


25°-35° 


35°-45 


25°-350 


35° -45 


2 


0.0243 


0.0147 


2.35 


1.76 


4 


0.0226 


0.0160 


2.43 


2.12 


10 


0.0181 


0.0153 


2.20 


2.20 


50 


0.0188 


0.0162 


2.58 


2.63 


100 


0.0176 


0.0169 


2.50 


2.82 


200 


0.0187 


0.0175 


2.68 


2.98 


400 


0.0178 


0.0156 


2.65 


2.73 


800 


0.0172 


0.0163 


2.63 


2.92 


.600 


0.0185 


0.0177 


2.81 


3.18 



37 



TABLE ZXXVII. - Comparison of Temperature Coefficients of 

Ammonium lodlc^e from 25^ to 55^ in Mixtures 
of Glyoerol and Water . 



V 


100 per oent . 


75 per cent. 


50 per 


25 per 


per 








cent . 


cent . 


cent . 


10 


0.1047 


0.0551 


0.0351 


0.0246 


0.0225 


50 


0.1061 


0.0572 


0.0353 


0.0248 


0.0187 


100 


0.1070 


0.0557 


0.0353 


0.0242 


0.0184 


200 


0.1082 


0.0558 


0.0360 


0.0256 


0.0212 


400 


0.1030 


0.0561 


0.0371 


0.0249 


0.0196 


800 


0.0923 


0.0560 


0.0364 


0.0261 


0.0202 


1600 


0.0964 


0.0557 


0.0360 


0.0269 


0.0193 



TABIE XXXVIII. - Comparison of Temperature Coefficients of 

Rubidium Bromide from 25 to 35° in Mixtures 
of Glycerol and Water . 



100 per cent. 75 per cent. 50 per cent 



10 
50 

100 
200 
400 
800 
1600 



0.1037 

0.1071 
0.1057 
0.1036 
0.1011 
0.1020 
0.1198 



0.0522 
0.0514 
0.0542 
0.0542 
0.0540 
0.0538 
0.0544 



0.0335 
0.0328 
0.0340 
0.0344 
0.0340 
0.0347 
0.0350 



25 per 


per 


cent . 


cent. 


0.0222 


0.0181 


0.0225 


0.0188 


0.0239 


0.0176 


0.0248 


0.0187 


0.0242 


0.0178 


0.0242 


0.0172 


0.0226 


0.0185 



TABLE ZZXIZ. - YiSQOSlty and Fluidity of Aromonlum Iodide in 
Glyoerol at 25^, 35^, 45° . 



Mol 



. cone. 


^ 25° 


^ 35° 




^45 


^25° 


^35° 


<^45° 


1.00 


4.399 


2.063 


1.071 


0.2273 


0.4847 


0.9335 


1.75 


4.769 


2.219 


1.139 


0.2097 


0.4506 


0.8782 


0.50 


5.119 


2.355 


1.205 


0.1953 


0.4246 


0.8295 


0.25 


5.498 


2.511 


1.275 


0.1819 


0.3982 


0.7841 


0.10 


5.766 


2.623 


1.325 


0.1734 


0.3812 


0.7545 



Solv. 5.826 2.648 1.332 0.1716 0.3776 0.7509 



TABLE XL. - Temperature Coefficients of Fluidity. 

350-45° 



0.093 
0.095 
0.095 
0.096 
0.098 
0.099 



Mol. cone. 


250-35° 


1.0 


0.113 


0.75 


0.115 


0.50 


0.117 


0.25 


0.119 


0.10 


0.120 


Solv. 


0.120 



TABLE XLI . - Ylscosity and Fluidity of Ammonium Iodide in 





Glycero 


1 at 55°, 


65°. 75° 


* 






Mol. cone. 


^ 55° 


^65° 


^750 


^55° 


^65° 


qy 75° 


1.00 


0.5927 


0.3623 


0.2264 


1.687 


2.760 


4.416 


0.75 


0.6215 


0.3772 


0.2344 


1.609 


2.651 


4.266 


0.50 


0.6540 


0.3850 


0.2424 


1.529 


2.597 


4.126 


0.25 


0.6807 


0.3963 


0.8516 


1.469 


2.523 


3.975 


0.10 


0.7060 


0.4028 


0.2577 


1.416 


2.482 


3.880 


Solv. 


0.7100 


0.4076 


0.2558 


1.408 


2.453 


3.909 



TABLE 


ZLII. 


- Temperature 


Coefficients of Fluidity. 


. Gonc 


!. 


45°-550 


550-65° 55°-750 


1.00 




0.081 


0.063 0.060 


0.75 




0.083 


0.065 0.061 


0.50 




0.084 


0.070 0.059 


0.25 




0.087 


0.072 0.058 


0.10 




0.087 


0.075 0.056 


Solv. 




0.067 


0.074 0.059 



40 



TABLE ZIIII. - Viscoaity and Fluicilty of Rubldltim Chloride 

in Glycerol at 25^, 35^, 45^ . 

Mol. cone. /^ 250 f 35° ^45° ^25° ^35° ^45° 



1.00 


5.240 


2.439 


1.264 


0.1908 


0.4099 


0.7910 


0.75 


5.351 


2.500 


1.282 


0.1869 


0.4000 


0.7801 


0.50 


5.542 


2.547 


1.307 


0.1804 


0.3926 


0.7651 


0.25 


5.711 


2.616 


1.328 


0.1751 


0.3823 


0.7531 


0.10 


5.818 


2.669 


1.346 


0.1719 


0.37 41 


0.7428 


SolY. 


5.880 


2.683 


1.350 


0.1701 


0.3727 


0.7407 



TABLE XLIV. - Temperature Coefficients of Fluidity. 



Mol. cone. 
1.00 
0.75 
0.50 
0.25 
0.10 
Solv. 



0.115 


0.095 


0.114 


0.095 


0.118 


0.095 


0.118 


0.097 


0.118 


0.098 


0.119 


0.099 



41 



TABLE ILY. - Visooslty and Fluidity of Rub id lug Chlorid e in 
Glycerol ajt 55^. 65^, 75^ . 

^ 65° 7 75° ^550 

0.4177 0.2595 1.456 

0.4195 0.2589 1.445 

0.4341 0.2604 1.420 

0.4423 0.2608 1.403 

0.4470 0.2606 1.384 

0.4505 0.26120 1.385 



Mol . cone . 


^56" 


1.00 


0.6867 


0.75 


0.6922 


0.50 


0.7043 


* 0.25 


0.7130 


0.10 


0.7224 


Solv. 


0.7218 



^65° 


(Z'75^ 


2.394 


3.854 


2.384 


3.862 


2.307 


3.840 


2.263 


3.834 


2.237 


3.831 


2.220 


3.828 



TABIS XLVI. 


- Temperature 


Goeff 


icients of Fluidity. 


Mol. cone. 


45°-55° 




55^-65° 650-75° 


1.00 


0.084 




0.064 0.061 


0.75 


0.085 




0.065 0.062 


0.50 


0.086 




0.062 0.069 


0.25 


0.086 




0.061 0.069 


0.10 


0.086 




0.068 0.071 


Solv. 


0.087 




0.060 0.072 



Gale, from N. 



42 



TABIE XLVII. - Viscosity and Fluidity of Rubidium Bromide in 
Glycerol at 25;^. 35^, 45^ . 



Mol . cone . 


1 25° 


^35° 


^45° 


(p 250 


^35° 


^450 


1.00 


4.965 


2.307 


1.199 


0.2014 


0.4335 


0.8339 


0.75 


5.177 


2.393 


1.228 


0.1931 


0.4178 


0.8146 


' 0.50 


5.388 


2.472 


1.274 


0.1856 


. 4044 


0.7849 


0.25 


5.623 


2.565 


1.284 


0.1778 


0.3898 


0.7785 


0.10 


5.858 


2.650 


1.338 


0.1707 


0.3773 


0.7473 


Solv. 


5.885 


2.664 


1.358 


0.1699 


0.3754 


0.7359 



TABLE ZLVIII. - 


- Tempo 


rature Coefficients. 








25^-35° 


350-45° 


1.00 




0.115 


0.092 


0.75 




0.116 


0.095 


0.50 




0.118 


0.094 


0.25 




0.114 


0.099 


0.10 




0.121 


0.098 


Solv. 




0.121 


0.096 



* Calculated values fran the K. sol. 



*o 



TABLE XLIX. - Viscosity and Fluidity of Rubidium Bromide in 





Glycerol at 55° 


, 65°-750 








IloI. cone. 


^550 


^65° 


^75° 


^55° 


^65° 


f 75<* 


1.00 


0.6483 


0.3967 


0.2457 


1.542 


2.520 


4.070 


0.75 


0.6603 


0.4041 


0.2484 


1.514 


2.474 


4.025 


0.50 


0.6789 


0.4108 


0.2528 


1.473 


2.434 


3.955 


0.25 


0.6990 


0.4146 


0.2554 


1.430 


2.412 


3.915 


0.10 


0.7096 


0.4226 


0.2589 


1.409 


2.366 


3.863 


Solv. 


0.7121 


0.4259 


0.2604 


1.404 


2.348 


3.840 



TABT.y. LZ. - 


Temperature 


Goeffici 


ents. 






45°-55° 




55°-65° 


65^-750 


1.00 


0.085 




0.063 


0.062 


0.75 


0.086 




0.063 


0.063 


0.50 


0.084 




0.065 


0.062 


0.25 


0.084 




0.069 


0.062 


0.10 


0.089" 




0.068 


0.063 


Solv. 


0.091 




0.067 


0.068 



'^O 



44 



TABLE LZI. - YlSGOSlty anci Fluidity of Eu"biaiiim loaide in 





Glyoero 


\ at 25° 


. 35°, 


45°. 






. cone . 


/2 25° 


^350 


^450 


^25° 


(^350 


^450 


1.00 


4.613 


2.163 


1.121 


0.2168 


0.4623 


0.8916 


0.75 


4.912 


2.292 


1.181 


0.2036 


0.4362 


0.8468 


0.50 


5.159 


2.365 


1.209 


0.1938 


0.4228 


0.8269 


0.25 


5.566 


2.554 


1.294 


0.1797 


0.3915 


0.7729 


0.10 


5.769 


2.628 


1.328 


0.1733 


0.3804 


0.7529 


Solv. 


5.854 


2.669 


1.341 


0.1708 


0.3746 


0.7457 



TABIE 


1 LXII 


Mol. 


cone. 


1. 


,00 


0. 


.75 


0. 


.50 


0, 


.25 


0, 


.10 


Solv. 



- Temperature Coefficients of Fluidity . 



25°-350 

0.113 
0.114 
0.118 
0.118 
0.119 
0.119 



350-45° 

0.093 
0.096 
0.096 
0.097 
0.098 
0.099 



45 



TABLE LXIII . - Viscosity and Fluidity of Rubiditup Iodide in 







Glycerol at 55' 


°. 65°. 


750. 






• 


cono. 


^560 


^650 


^75° 


^55° 


^65° 


^75° 


1, 


.00 


0.6184 


0.3763 


0.2355 


1.617 


2.657 


4.246 


0, 


.75 


0.6436 


0.3892 


0.2420 


1.554 


2.569 


4.132 


0. 


.50 


0.6585 


0.3981 


0.2472 


1.519 


2.512 


4.044 


0, 


.25 


0.6955 


0.4132 


. 2548 


1.422 


2.420 


3.924 





.10 


0.7102 


0.4236 


0.2566 


1.408 


2.360 


3.898 


s< 


DlV. 


0.7144 


0.4243 


0.2581 


1.400 


2.357 


3.874 



TABLE LXIV. - Temperature Coefficients of Fluidity 



Mol. cone. 


45°-55° 


55°-65° 


65°-75° 


1.00 


0.081 


0.064 


0.060 


0.75 


0.083 


0.065 


0.061 


0.50 


0.084 


0.065 


0.061 


0.25 


0.084 


0.070 


0.062 


0.10 


0.087 


0.068 


0.065 


Solv. 


0.088 


0.068 


0.064 



46 



TABLE LXV . - Yisoosity and Fluidity of Rubidliim Nitrate in 
Glycerol at 25°, 35°, 45°. 



Mol, 



cono. >l 25° y^ 35° /J 45° (0 25° CI) 35° 



45 



0.50 


4.639 


2.355 


1.204 


0.2156 


0.4246 


0.8307 


0.25 


5.571 


2.552 


1.294 


0.1795 


0.3918 


0.7727 


0.10 


5.787 


2.634 


1.338 


0.1728 


0.3796 


0.7473 


Solv. 


5.854 


2.669 


1.341 


0.1708 


0.3746 


0.7457 



TABLE LXVI. - 


■ Temperature Coeff 


icie 


nts 


of 


Fluidity 


Mol. cono. 


25°-35° 








35°-45° 


0.50 


0.097 








0.096 


0.25 


0.118 








0.098 


0.10 


0.120 








0.097 


Solv. 


0.119 








0.099 



47 



TABLE LZVII . - Vlaooslty and Fluidity of Rubidium Nitrate 
is Glycerol at 550 . 65° , 75° . 



Mol. oonc. 


^55° 


^65° 


^760 


^55° 


^65° 


(p 75 


0.50 


0.6530 


0.3982 


0.2471 


1.531 


2.511 


4.046 


0.25 


0.6955 


0.4179 


0.2561 


1.438 


2.393 


3.904 


0.10 


0.7099 


0.4237 


0.2570 


1.409 


2.360 


3.891 


Solv. 


0.7144 


0.4243 


0.2581 


1.400 


2.357 


3.874 



TABLE LXVIII. - Temperature Coefficients of Fluidity 



Mol. cone. 


45°-55° 


550-65° 


65°-75° 


0.50 


0.084 


0.064 


0.061 


0.25 


0.086 


0.066 


0.063 


0.10 


0.088 


0.068 


0.064 


Solv. 


0.088 


0.068 


0.064 



48 



TABLE LXT7. 


- Viscos 


ity and Fluidity of 


Ammonium Iodide 


in 




75^ Glycerol with water 


at 250. 


35°. 45°. 




Mol . cone . 


1 25° 


^36° 


q 45° 




^^25® 


^35^ 


^450 


1.00 


0.2548 


0.1580 


0.1049 




3.925 


6.327 


9.529 


0.75 


0.2703 


0.1656 


0.1094 




3.700 


6.039 


9.138 


0.50 


0.2873 


0.1754 


0.1143 




3.481 


5.700 


8.749 


0.25 


0.3058 


0.1842 


0.1193 




3.270 


5.429 


8.383 


0.10 


0.3097 


0.1873 


0.1204 




3.229 


5.338 


8.302 


Solv. 


0.3174 


0.1902 


0.1220 




3.151 


5.259 


8.197 



TABLE LXZ. - Temperature Coefficients of Fluidity . 



Mol. cone. 
1.00 
0.75 
0.50 
0.25 
0.10 
Solv. 



250.35<> 


35O-450 


0.0612 


0.0506 


0.0632 


0.0513 


0.0637 


0.0535 


0.0660 


0.0544 


0.0653 


0.0555 


0.0669 


0.0559 



TABLE LXZI . - Viscosity and Fluidity of Ammonium Iodide in 

50 per cent Glycerol with water at 25° . 35° , 45° . 



Mol. cone. 


? 250 


^350 


1.00 


0.05335 


0.03838 


0.75 


0.05534 


0.03950 


0.50 


0.05V 93 


0.04089 


0.25 


0.06029 


0.04230 


0.10 


0.06064 


0.04260 


Solv. 


0.06174 


0.04299 



f 



45^ 



25^ 



(^-'350 ^^45° 



0.02821 18.74 

0.02885 18.07 

0.02967 17.26 

0.03182 16.59 

0.03092 16.49 

0.03092 16.20 



26.05 
25.32 
24.46 
23.64 
23.47 
23.26 



35.45 
34.66 
33.70 
31.43 
32 ."34 
32.34 



TABLE LZZII. - Temperature Coefficients of Fluidity . 



Mol. cone. 



E5°-35° 



35O-45O 



1.00 
0.75 
0.50 
0.25 
0.10 
Solv. 



0.0390 
0.0401 
0.0417 
0.0425 
0.0423 
0.0432 



0.0361 
0.0369 
0.0378 
0.0329 
0.0379 
0.0390 



. 1 



TABLE LXZIII . - Viscosity and fluidity of AminoniTim Iodide 

in 25 per pent Glycerol with water at 
25° . 55Q . 450 , 



Mol. cone. // 25° 



1.00 
0.75 
0.50 
0.25 
0.10 
Solv. 



0.01802 
0.01843 
0.01910 
0.01973 
0.01997 
0.02018 



/7 350 





/7 45° ^^25° ^35° <^450 



0.01406 0.01124 55.49 

0.01436 0.01147 54.26 

0.01464 0.01157 52.36 

0.01501 0.01180 50.68 

0.01510 0.01182 50.07 

0.01525 0.01189 49.55 



71.12 88.97 

69.64 87.18 

68.31 86.43 

66.62 84.75 

66.22 84.60 

65.57 84.10 



TABLE LZXIV. - Temperature Coefficients of Fluidity . 



Mol. 


cone. 


1. 


00 


0. 


75 


0. 


50 


0. 


25 


0, 


10 


Solv. 



250-350 

0.0282 
0.0283 
0.0305 
0.0314 
0.0322 
0.0333 



350-45° 

0.0251 
0.0252 
0.0265 
0.0272 
0.0278 
0.0282 



51 



TABLE LZZV. - Vlscoalty 6f Ammonltim Iodide in Water at 
25°, 35°, 45°. 



Mol, 



!onc. ^ 25° /^ 35° 



f 



45' 



^25° 



r 



35' 



f^'45< 



1.00 


0.00838 


0.00695 


0.00584 


119.3 


143.9 


178.2 


0.75 


0.00869 


0.00701 


0.00589 


115.1 


142.7 


169.8 


0.50 


0.00871 


0.00705 


0.00595 


114.7 


141.7 


168.0 


0.25 


0.00877 


0.00712 


0.00590 


114.0 


140.4 


169.4 


0.10 


0.00889 


0.00717 


0.00597 


112.4 


139.4 


167.5 


Solv. 


0.00891 


0.00720 


0.00597 


112.2 


138.9 


167.5 



TABLE LZZYI . - Temperature Coefficients of Fluidity , 



Mol. cone. 



25°-350 



35°-450 



1.00 
0.75 
0.50 
0.25 
0.10 
Solv. 



0.0206 
0.0240 
0.0235 
0.0232 
0.0240 
0.0238 



0.0170 
0.0190 
0.0185 
0.0206 
0.0217 
0.0205 



TABLE LXZVII. - Viscosity and Fluidity of Rubidium Bromide 





in 


75 per oent Gl^'cero 


1 with 


Water. 




Mol. oonc. 


q 25° 


^sbo 


^450 


(/? 25C 


• ^'35° 


^45' 


1.00 


0.2753 


0.1702 


0.1137 


3.627 


5.874 


8.797 


0.75 


0.2844 


0.1756 


0.1152 


3.516 


5.694 


8.683 


0.50 


0.2944 


0.1795 


0.1169 


3.396 


5.570 


8.556 


0.25 


0.3036 


0.1838 


0.1168 


3.293 


5.441 


8.558 


0.10 


0.3108 


0.1877 


0.1184 


3.217 


5.327 


8.432 


Solv. 


0.3135 


0.1880 


0.1209 


3.189 


5.319 


8.270 



TABIE LXZVIII. - Temperature Ooeff ioients of Fluidity . 



Mol. cone. 


25*^-35° 


35O-45O 


1.00 


0.0619 


0.0496 


0.75 


0.0619 


0.0525 


0.50 


0.0640 


0.0536 


0.25 


0.0652 


0.0573 


0.10 


0.0656 


0.0583 


Solv. 


0.0668 


0.0555 



TABLE LXXIX. - Viscosity and Fluidity of RubidjLum Bromide 





in 


50 per cent 


Glycerol 


with Wat 


er . 




Mol. cone 


. n 25° 


/I 35° 


^45° 


{f Zh^ 


^/ 35° 


, 45 

/ 


1.00 


0.05514 


0.03958 


0.02906 


18.14 


25.27 


34.41 


0.75 


0.05625 


0.04035 


0.02946 


17.78 


24.78 


33.95 


0.50 


0.05791 


0.04064 


0.03014 


17.27 


24.61 


33.18 


0.25 


0.05915 


0.04194 


0.03018 


16.91 


23.90 


33.13 


0.10 


0.05986 


0.04E07 


0.03029 


16.71 


23.77 


33.01 


Solv. 


0.06021 


0.04229 


0.03035 


16.61 


23.65 


32.95 



TABIE ISJS., - Temperature Goefficients of Fluidity . 



Mol. cone. 



25 -35° 



35°-45° 



1.00 
0.75 
0.50 
0.25 
0.10 
Solv. 



0.0393 
. 0394 
0.0425 
0.0414 
0.0423 
0.0424 



0.0362 
0.0370 
0.0348 
0.0386 
0.0389 
0.0393 



54 



TABIE IZZXI. - Viscosity and Fluiclity of Rubidium Bromide 

in 25 per cent Glycerol with Water . 

Mol. cone. .^ 25° /7 35° /; 45° ^25° ^35° (f 45° 



0.50 


0.01931 


0.01492 


0.01179 


51.80 


67.03 


84.81 


0.25 


0.01970 


0.01605 


0.01186 


50.76 


66.44 


84.30 


0.10 


0.01996 


0.01518 


0.01190 


50.09 


65.88 


84-06 


Solv. 


0.02017 


0.01523 


0.01191 


49.59 


65 ./64 


83.97 



TABIE LZXSII. - Temperature Goeffioients of Fluidity , 



Mol. 


cone 


0, 


.50 


0, 


.25 


0, 


.10 


Solv. 



250-35° 

0.0294 

0.0309 
0.0315 
0.0324 



35°-45° 

0.0265 
0.0269 
0.0276 
0.0279 



55 



TABIE IXXZIII. - Yisooslty and Fluidity of Rubidium Bromide 





in 


Water at 


25°. 35°. 


450. 






Mol.conc. 


^£50 


/7350 


f 450 


^^250 


^35° 


^450 


0.50 


0.00872 


0.00718 


0.00608 


114.7 


139.4 


164.3 


0.25 


0.00882 


0.007-20 


0.00600 


113.2 


138.8 


166.7 


0.10 


0.00880 


0.00717 


0.00596 


113.6 


139.4 


167.7 


Solv. 


0.00891 


0.00720 


0.00597 


112.2 


138.9 


167.5 



TABLE LXZZIV. - Teaperature Coefficients of Fluidity . 



Mol. cone. 



25°-350 



35°-450 



0.50 
0.25 
0.10 
Solv. 



0.0215 
0.0226 
0.0227 
0.0238 



0.0179 
0.0201 
0.0203 
0.0205 



00 



TABLE LXXZV.- Percentage Increase in fluidity of Rormal 





So 


luti 


ons 


in 


Glycerol 


at 


25°, 


35°, 45°. 




£5° 








35° 






45° 


UE^I 


32.4 








28.4 






22.9 


Rbl 


26.3 








23.4 






19.6 


RbBr 


18.5 








15.4 






11.9 


EbCl 


12.2 








9.9 






6.8 



TABLE LXUMl. - Comparison of Percentage Increase in Fluidity 





of 


Gl7^c 


erol by 


Ammonium 


Iodide and Rubidium 




loa 


Lide 


at 25°. 






Mol. cone 






KH4I 




Rbl 


1.0 






32.4 




26.3 


0.75 






22.2 




19.2 


0.50 






13.9 




13.1 


0.25 






6.0 




5.2 


0.10 






1.1 




1.5 



TABLE LZZZVII. - Percentage Increase in Fluidity of Glycerol 

Water Mixtures at 25°. 



50^ 25^ Water, 





Mol 


. cone. 


Glycerol 


im^i 




1 


32.4 


RbBr 




1 


18.5 



24.5 15.7 11.9 5.3 
11.2 9.2 (8.8) (4.5) 



OEFT. EXPEniMENT*!. Ef<GINECBIVG, BIBLEY COCltOEi mWNELL UNI\FERBrrf. 




75 50 25 

Per cent. Glycerol 



Fig. I— Conductivity of Amiioonium Iodide in Glycerol-Water at 25' 



PEFT. EXPEBlMgWTAL gWfllNEEHIWQ, 8IBLEV eOClEQgt CORNELL DHIVEHaiTT. 




. ^ ft. C- CAflrENTUI. ITHACA N. t. _ -i, 

I do 7S 



50 25 

Per cent. Glycerol 



Fig^II- Conductivity of Rub.idiun Bromide in Glycerol-Water at 25' 



■I Vivmt ■ir3i'.'3iuv3 1 •« 



4 'J 







25 



3 
X 

H 

■a 

H 
D 

H 



20 



t5 : 



1 



t 




T 



Volume Concentration 

Fig III- Conductivity and Fluidity of Rubidiuir Iodide in Glycerol 
a-t- 2b - 



DCPT. EyotRlMENTiy. EMGINFrnrNQ, glBLEV COUEGE, CORNELL UNIVERSITr. 


















































A f> 1 . 1 1 , M 1 , , : 1 : . 1 , 1 , 1 t ■ 




,>^ , 1 ■ 1 r . . 1 . 1 . 1 I 1 1 i ■ [ : 






























O \ 1 t 1 1 1 ! 1 ■ 1 ! 1 ' 1 1 1 1 1 1 M 1 ■ 1 1 1 1 I 1 1 1 1 1 1 M 1 1 . 1 MM 










' ■> ' ! ' 1 N 1 ' i 1 i ! M ' - . hi 1 r- : , , , i i 1 1 i 1 1 t 
































Q i 1 ■ 1 1 'III, F*-^.^ '1 ( 1 1 i 1 '-i— --1 1.1 1 1 1 1 . I 1 F ! 1 








< < 1 '1 1 1 1 1 1 1 t < 1 1 1 M ii f 1 1 1 




















































1 i 1 1 1 ' ' ' 1 ' ' 1 ' 














^°- . . -- M ; _L 1 _U_L^ L i' L^ 
























^ ' ■ 1 I 1 ] 1 ■ 11 til 1 t ■ 1 ( i 1 1 1 1 1 1 I ' > > 1 1 M 1 ,■ 1 
























f-J on 1 > , ■ M II II' M 1 . M 1 M ' ! : ' 1 , 


























-■"T rr ^^-1 — ■ --|- . . . .-■— ': - -; gg n | j'^»7-^ | ■ — , ■ ■ ■ — ■ . ' • j ■ ■ m\ 15-i-r-t- J- — 
























i [.<C CMlflU fjl. ITrtA>.n N. 1. 



I 1.3 2 



10 



Vftlnme Concentration 
Fig,. IV - Conductivity and Fluidity of Ammonium Iodide in Glycerol 
at 25". 



, eXFUIIMNTAL KNOIIttmiM ItKeV eeUt«i COWWeH. OWIVgWITT. 




I 00 



75 



50 25 

Percent. Glycerol 
Fig.V- Specific Conductivity and Fluidity of Glycerol-?/ater Mixtures 

at Z^" 



57 



DISCUSSION OF RESULTS 



The hypothesis of Dutoit and Aston, already referred 
to makes the dissociating power of a solvent a function of 
its own association. The degree of association of a solvent 
by the method of Ramsay and Shields has been shown to decrease 
withrisein temperature. Therefore, the increase in condnctiv- 
Ity usually observed with rise in temperature, can not be due to 

an Increase in the number of ions present but must be caused 

(1) 
by an increase in the velocity of those ions. As Guy and 

others have already brought out, the change in the velocity of 
the ions withrisein temperature is to be ascribed to the change 
in the viscosity of the media surrounding the ions and in some 
instances, to the change In the mass of the ionic complexes 
formed by the l:.ns and a certain number of molecules of the 
solvent . 

Previous workers with glycerol as a solvent have already 
noted the enormous increase in conductivity of solutions In 
It withrisein tenqperature. V.hile Guy has found some evidence 
for the existence of glycerolates, the writer believes the 
chief conditioning factor to be the change in the viscosity 
of the solvent. It is with the viscosity phenomena and chief- 
ly with that of the lowering of the viscosity of glycerol by 
certain salts that this investigation has had to deal. 

(1) Loc. cit. 



J r D t 



'S 



58 



Both conductivity and viscosity data have been obtain- 
ed on the various salts studied and are presented in tabular 
form with accompanying tables of temperature coefficients. ' 

Tables I to XX, inclusive, contain the molecular conduc- 
tivities at ten degree intervals from 26° to 75° of ammonium 
Iodide and of the several rubidium salts which I have studied 
in pure glycerol as a solvent, in agreement with the work of 
preceding invest igatots, viz., Schmidt and Guy, all the values 
for /'/ are seen to be extremely low, much smaller than corres- 
ponding values in water. These values show a marked increase , 
with rise in temperature and in the more dilute solutions 
{ll/lO to ir/ieoo) a regular Increase with dilution. It is to ' 
be noted that in the more concentrated solutions, especially 
of the iodides, a decrease in conductivity takes place, the mini- 
mum lying as a rule close to the value for the n/lO solution. ' 
A discussion of this phenomenon will be taken up after a review 
of viscosity data. 

The corresponding temperature coefficients of all the 
salts studied both in conductivity units and in percentages are 
of the same order of magnitude and show the same relative in- 
crease with increased dilution. This is to be expected since j 
these salts are all binary electrolytes, and since all belong : 
to that class whose cations possessing the largest atomic volumes, 
have been shown to have little or no hydrating power in water. j 
Such is not the case with ternary electrolytes in glycerol and 
especially with salts of calcium, strontium .barium and cobalt, ] 
the explanation of which has been fully given by Guy who bases ; 



aic 



oy 



his conclusions on the solvate theory. He points out that 
If there be solvation this should be more marked in the more 
dilute solutions where the amount of solvent per ion is great- 
est. Hence a change in tenperature would produce the greatest 
effect where the solvation was greatest, viz., in the more di- 
lute solutions and in solutions of those salts which have the 
greatest power of solvation. 

The percent temperature coefficients are seen to be very 



large, being from ten to eleven percent between 25 and 35 . 
They decrease rapidly with rise in temperature, the value be- 
tween 65° and 75 lying between four and a half and fjve per- 
cent- This may be partially accounted for by the enormous de- 
crease in the viscosity of glycerol with rise in temperature. 
At 25 glycerol has a viscosity approximately 660 tlEes that 
of water, while at 35 the value is 370 times that of water, 
but little more than half as great. At 75 the ratio falls to I 
70, In no other comrron solvent are the temperature coefficients 
of conductivity so great and the above ratios will show to some 
extent why this should be the case. ' 

Tables XZI to ZXXVI, inclusive, contain the molecular con- j 
ductivities at 25 , 35 and 45 of ammonium iodide and rubidium 
bromide in mixtures of glycerol with water. Figures 1 and 2 
express these results graphically. The solvents were prepared 
by diluting n. cc.of glycerol to one liter and denoting the 
resulting solvent as a mixture of n. percent, glycerol, with 
water. 



60 



It will be seen that the condtictivity curves of such 
mixtures show a decided sagging, the conductivity values be- 
ing always less than would be expected from the law of aver- 
ages. The explanation of this has been given by Jones and 

(1) (1) I 

Lindsey and Jones and Murray' for mixtures of water with 

the alcohols and has been extended to mixtures containing gly- 
cerol by Guy. A statement of the facts alone is necessary since 
reference has previously been made to this phenomenon. V'hen 
two highly associated liquids are mixed, or, to take a specif- 
ic instance, when glycerol is mixed with water, it has been shown 
that in such a case the properties of the mixture are not addi- , 
tlve, each solvent tending to break down the association of | 
the other; the combined dissociating effect of the two being 
less than would be expected had there been no such mutual dimin- 
ution of the association. Guy has shown that in the case i 
of glycerol mixtures with the alcohols, the diminution of the 
association takes place largely in the case of the glycerol. 

In Tables XXXVII and XXXVIII a coEparison is made of the 
temperature coefficients at £5°-35° of the two salts which we 
have studied in mixed solvents. These are seen to diminish 
rapidly with, addition of water, passing from 10 percent in pure 
glycerol to 2 percent in 257o glycerol. 

The curve representing the specific conductivities of 
the various mixtures from glycerol to pure water is shown in 
Pig. 3. The values for 50% and 257o glycerol are larger than 
that for water, -^-'his Is probably due to the presence of a 
few OH ions split off from the glycerol by action of the v/ater. 
'1 J Loc. cit . 



-r'st'^ 



61 



NEGATIVE VISCOSITY 



A historical sketch of previous work in viscosity has 
already been given in the introductory part of this memoir. 
It Is necessary therefore to take up here only the more im- 
portant points. 

Veazey's apparently satisfactory explanation of the phe- 
nomenon of negative viscosity has received ample corroboration 
by later workers. It will be remembered that he attributed 
the lowering of the viscosity of a solvent by a dissolved sub- 
stance to the lessening in the skin friction between the mole- 
cules of the solvent and the molecules or ions of the solute in 
a given volume of the solution, because of the large atomic vol- 
umes of the cations, viz., potassium, rubidium and caseium, 
these three metals occupying the maxima on the atomic volume 
curve. Subsequent investigations have shown that certain ammo- 
nium salts in organic solvents, such as glycerol, are to be in- 
cluded in this category. Although we may not speak of the am- 
monium radicle IIH. as having atomic volume, still it is well 
known that it possesses chemical properties closely allied to 
the alkali metals. 

It is not surprising, therefore, to find negative viscos- 
eS-iec ts 
ity^ produced by ammonium salts, and from observations made by 

Guy on ammonium bromide, and from my own observations on am- 
monium iodide it is probable that the molecular complex IIH^ 
should occupy a place on the volume curve close to rubidium. 



62 



In Tables XXXIX to LXVIII, inclnslve, the viscosities 

and fluidities of ammonium iodide and of rubidium chloride, 

(1) 

bromide, iodide and nitrate in pure glycerol at 25 to 

75 are given for a range of dilution from H to u/lO. In 

every case the viscosity of the solution is less than that of 

the solvent . Even at 75 , rubidium chloride which increases 

the fluidity the least shows a positive fluidity coefficient 

of .3^ for the N/10 solution. 

A table of percent temperature coefficients of fluidity 
is given with each table of viscosities. These are seen to be 
almost equal to the temperature coefficients of conductivity but 
in every case are somewhat larger, ^'his is to be accounted for 
by the decrease in association of the solvent with rise in tem- 
perature causing a decrease in the ionization of the solute and 
therefore a smaller conductive capacity. 2)his v/ould in part 
offset the increase in conductivity due to an increase in the 
velocity of the ions because of the decrease in viscosity of 
the solvent withrisein temperatiire. 

The greatest viscosity lowering or increase in fluidity 
is to be observed in the case of the normal solution. This 
is obvious since the effect is proportional to the concentra- 
tion, ^he dilution curve does not pass through a minimum but 
becomes asymtotic to that of the solvent at dilutions beyond 
the 11/50. The percentage increase in fluidity becomes less 
also with rise in temperature, which may be accounted for by 



(1) li:/2 sol. saturated at 20°. 



b ti 



iRT" 



O^ 



63 



the change In the molecular aggregates of the solvent and by 
the greater effect of temperature than of the dissolved salt 
on the viscosity of the solvent. 

With the above facts in view, it is possible to explain 
the minima found at low temperatures in the conductivity curves 
for the concentrated solutions. These minima are more marked 
at 25 and in the case of those salts which give the greatest 
lowering of the viscosity of glycerol, viz., ammonium and 
rubidium iodides. In the concentrated solution (U - H/4) the 
ionization is nearly constant, while the negative viscosity 
effect decreases with increased dilution. 

Reference to Pig. 3 will show that the conductivity and 
fluidity curves at 25 for rubidium iodide are practically par- 
allel up to and through the U/lO solution. Beyond that dilu- 
tion the increased ionization causes a rise in the conductivity 
curve while the fluidity curve becomes the asyiiiitoi"e of the 
solvent. Here we have conductivity varying directly as the 
fluidity or inversely as the viscosity. It is of interest to 
observe that a salt can lower the viscosity of a solvent to 
such an extent as to increase its own conductivity in that 
solvent' Fig. 4 shows similar results witli ammonium iodide. 

Table LZXXV shows the relative percentage increase in 
fluidity produced by normal solutions of the various rubidium 
salts and of ammonium iodide at 25°-45°. It is evident that 
of the halogen salts of rubidium the iodide produces the great- 
est change in fluidity, followed by the bromide, then the chlor- 
ide. This may be explained by the fact that when the cation. 



me 



Sfl3.f/31. 



ew r 



here rubidium, to which the increase in fluidity is mainly 
due, remains the same, the negative viscosity effect is a 
function of the molecular volumes of the salt in question. 

If we divide the molecular weights of the three halogen 
salts by their densities referred to water as a unit, we ob- 
tain the following values: 

Rbl. ^^fjH - 7.02; EbBr ^^^^ =5.95; RbCl, i^|^ = 
5.496. Reference to the table will show that the experimental 
data is in accord with this. rubidium iodide at 25° producing 
a percent increase in fluidity of 26.3, rubidium bromide 18.5 
and rubidium chloride 12.2. It was impossible to prepare a 
normal solution of rubidium nitrate in glycerol at the normal 
temperature 20°. The ll/2 solution was nearly saturated at 
that temperature and shows somewhat greater negative viscosi- 
ty coefficients than would be expected. 

The N/4 solution, however, gives values between that 
of rubidium bromide and iodide which is to be expected from 
its molecular volume. Ho adequate explanation can be of- 
fered for the apparently abnormal negative viscosity coef- 
ficients of ammonium iodide in glycerol. 

In Table IZXXVI is given the percentage increase in fluid- 
ity at 25° produced by the two salts showing the most marked 
negative viscosity effect, viz., rubidium iodide and ammonium 
iodide over the range of dilution studied. That the increase 
in fluidity is not exactly proportional to the concentration 
may be due to the slight increase in ionization in the more 
dilute solution the effect of the anions tending to offset 



65 



that of the cation. 

Tables LXIX to LXZXIV, Inclusive, show the viscosities 
and fluidities of rubidium bromide and annnonium iodide in 
glycerol-water mixtures at 25°, 35 -45 . The addition of 
water to glycerol causes an enormous increase in fluidity. 
The curve representing the fluidity changes with decreasing 
percentages of glycerol shown in Pig. 5 is strikingly simi- 
lar to the conductivity curves in those mixtures, (Flgs.l & 2). 

The salts studied show negative viscosity in the glycerol 
water mixtures and in pure water at low temperatures. In 
water at 45°, rubidium bromide shows a tendency to pass over 
to positive viscosity altho the transition is not very mark- 
ed . 

The last Table (LZXXVII) gives a comparison of the per- 
centage increase in fluidity produced by normal solution of 
the two salts in glycerol-water mixtures at 25 . The values 
do not follow the law of averages in such mixtures out are 
lower* -i-'his is in all probability due to the increased ioni- 
zation in the mixed solvents, and also to the breaking down of 
the molecular complexes of the solvent which would In both 
cases give ultimate particles with greater frictional sur- 
faces . 



66 



SUMIMRY 



The following points have either been confirmed or 
brought out in this dissertation; 

1. Conductivity values in glycerol are extremely 
small but show regular increase with rise in tempera- 
ture and except in special cases, with dilution. 

2. In the case of salts producing a marked lower- 
ing of the viscosity of the solvent, a minimum In the 
conductivity curve of the concentrated solutions has been 
noted, the conductivity varying directly with the fluidity. 

3» Conductivities in glycerol-water mixtures do not 
follow the law of averages, but are always lower. 

4. Rubidium salts produce a phenomenal lowering of 
the viscosity of glycerol, much greater than that of corres- . 
ponding potassium salts. 

5« Ammonium salts seem more closely allied to rubid- 
ium than to potassium in their effect on the viscosity of 
a solvent like glycerol. 

6. The percentage Increase in fluidity of the solvent 
prodiiced by the dissolved salt becomes less with rise in tem- 
perature and with dilution. 



* 



'\ 



67 



7. Kubidium salts In pure glycerol show no tendency 
to produce positive viscosity even at 75 . 

8. Curves representing fluidity and conductivity 
In mixtures of glycerol and water show marked similarity 
over the range of temperature studied. 



68 



BIOGRAPHY 



Paul Bell Davis, the author of this dissertation, 
was born in 'Test Liberty, Logan County, Ohio, August 
15th, 1889. At an early age, he removed with his par- 
ents to Salem, Virginia, and in the public schools of 
this town he received his preliminary training. After 
studying one year at the Salem High School, he enter- 
ed the freshman class of Roanoke College in the fall 
of 1904. From this institution he received the degree 
of Bachelor of Arts in 1908. 

During the year 1908-09, he was assistant in chem- 
istry and was awarded the degree of Master of Arts in 
June 1909. In the fall of 1909, he entered the Johns 
Hopkins University as a graduate student in chemistry. 
His subordinate subjects were physical chemistry and 
mineralogy. 



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